Performability analysis of non-repairable multicomponent systems using order statistics

Performability, a composite measure that integrates both performance and reliability, has been deemed to be essential in evaluating systems that are capable of trading off performance for reliability under component failures. For non-repairable systems, the goal is to evaluate the distribution or moments of some accumulated reward (performance) defined on a stochastic process that characterizes the different configurations, as successive faults appear. Instead of assuming that the distributions of sojourn time at various configurations are known, we deduce them from the distributions of the individual component lifetime. We allow lifetimes to be arbitrary but assume that they are independent from one component to another. Knowledge of the reward rates in different configurations allows us to relate the sojourn times to the order statistics of the component lifetimes. We then solve for the distributions of the order statistics. The approach is illustrated in context of a parallel system made up of identical components